SNAKING PHENOMENA IN DICE LATTICE

• Main Author: Nathanael, Daniel
• Format: Final Project
• Language: Indonesia
• Online Access: https://digilib.itb.ac.id/gdl/view/64537
• Institution: Institut Teknologi Bandung

This final project studies the effect of different bonding powers in a lattice structure. The model we are using to portray the bonding powers between particles in the said structure is Allen-Cahn equation, as formulated by C. Chong and D. E. Pelinovsky (Chong dkk., 2012). We are going to search the solutions for the formula in two domains, in 1-D domain and 2-D domain. Particularly, we are interested in studying the equilibrium points in 2-D domain, as we can represent the domain into a pattern that is more accurate to portray a lattice. The solutions itself is going to be sought using numerical continuation, then the obtained numerical solutions are going to be compared with analytical solutions. Simulation with this method require a coefficient called bifurcation coefficient and accurate initial solutions. Therefore, we are going to conduct a simulation to search for the initial solutions first. After that, we are also going to search the stability of Allen-Cahn equation using a Laplacian matrix to obtain the eigenvalues. The stability of equlibrium solutions then are going to be plotted so that we can see the behavior of its linear stability. The obtained numerical solutions are also going to be plotted so that its behavior can be seen. The shape of the plot resembles a snake hence named snaking. This exact behavior is what we are trying to analyze and explain its effect physically to mineral structure.